Integration (1 Viewer)

[yeyjasminetime]

Hi I've attached a photo of the question because it's a bit hard to type up.

I can work the question out until the end where I'm not sure how the e substitutes.



Thanks in advanced!

 

[Sy123]

One doesn't really need to do substitution, you just need to recognise





This is a 2U concept

-

However if you are intent on using a substituion



To get the limit that replaces -e, we sub in -e into x, that means

is the new limit

 

[yeyjasminetime]

I mean when you sub -e into x-x^3 what does it equate to?

 

[yeyjasminetime]

The answers say Ln (6/e^2 -1) a1

 

[hit patel]

It is basically an approach as Sy123 says. This is easy way of doing this question by finding commonalities.

Ofc in other question that donot have f'x then you must use long division or splitting.

 

[Sy123]

I mean when you sub -e into x-x^3 what does it equate to?

So we get





Just using log properties here

 

[yeyjasminetime]

Thanks Sy123!

 

[mahmoudali]

So we get





Just using log properties here

dont you just:
[ln(x-x^3)] from -2 to -e
and you get ln(6) -ln(-e+e^3)= ln(6/(e(-1+e^2))) = ln(6/-1+e^2) - ln(e) hence that girls solution ln(6/e^2 -1) -1
im pretty sure she didnt want the u substitution method but its better that you show your supreme ways sy